article published yes S. Mathis author Lisa Annabelle Bugnet author d9edb345-f866-11ec-9b37-d119b52345010000-0003-0142-4000 LiBu department Context. Space asteroseismology is revolutionizing our knowledge of the internal structure and dynamics of stars. A breakthrough is ongoing with the recent discoveries of signatures of strong magnetic fields in the core of red giant stars. The key signature for such a detection is the asymmetry these fields induce in the frequency splittings of observed dipolar mixed gravito-acoustic modes. Aims. We investigate the ability of the observed asymmetries of the frequency splittings of dipolar mixed modes to constrain the geometrical properties of deep magnetic fields. Methods. We used the powerful analytical Racah-Wigner algebra used in quantum mechanics to characterize the geometrical couplings of dipolar mixed oscillation modes with various realistically plausible topologies of fossil magnetic fields. We also computed the induced perturbation of their frequencies. Results. First, in the case of an oblique magnetic dipole, we provide the exact analytical expression of the asymmetry as a function of the angle between the rotation and magnetic axes. Its value provides a direct measure of this angle. Second, considering a combination of axisymmetric dipolar and quadrupolar fields, we show how the asymmetry is blind to the unraveling of the relative strength and sign of each component. Finally, in the case of a given multipole, we show that a negative asymmetry is a signature of non-axisymmetric topologies. Conclusions. Asymmetries of dipolar mixed modes provide a key bit of information on the geometrical topology of deep fossil magnetic fields, but this is insufficient on its own. Asteroseismic constraints should therefore be combined with spectropolarimetric observations and numerical simulations, which aim to predict the more probable stable large-scale geometries. https://research-explorer.ista.ac.at/download/14256/14271/2023_AstronomyAstrophysics_Mathis.pdf application/pdfno EDP Sciences2023 eng 0004-6361 1432-0746 2306.11587 00104603770000710.1051/0004-6361/202346832 676 S. Mathis, L.A. Bugnet, Astronomy &#38; Astrophysics 676 (2023). S. Mathis and L. A. Bugnet, “Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields,” <i>Astronomy &#38; Astrophysics</i>, vol. 676. EDP Sciences, 2023. Mathis S, Bugnet LA. 2023. Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields. Astronomy &#38; Astrophysics. 676, L9. Mathis, S., &#38; Bugnet, L. A. (2023). Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields. <i>Astronomy &#38; Astrophysics</i>. EDP Sciences. <a href="https://doi.org/10.1051/0004-6361/202346832">https://doi.org/10.1051/0004-6361/202346832</a> Mathis S, Bugnet LA. Asymmetries of frequency splittings of dipolar mixed modes: A window on the topology of deep magnetic fields. <i>Astronomy &#38; Astrophysics</i>. 2023;676. doi:<a href="https://doi.org/10.1051/0004-6361/202346832">10.1051/0004-6361/202346832</a> Mathis, S., and Lisa Annabelle Bugnet. “Asymmetries of Frequency Splittings of Dipolar Mixed Modes: A Window on the Topology of Deep Magnetic Fields.” <i>Astronomy &#38; Astrophysics</i>, vol. 676, L9, EDP Sciences, 2023, doi:<a href="https://doi.org/10.1051/0004-6361/202346832">10.1051/0004-6361/202346832</a>. Mathis, S., and Lisa Annabelle Bugnet. “Asymmetries of Frequency Splittings of Dipolar Mixed Modes: A Window on the Topology of Deep Magnetic Fields.” <i>Astronomy &#38; Astrophysics</i>. EDP Sciences, 2023. <a href="https://doi.org/10.1051/0004-6361/202346832">https://doi.org/10.1051/0004-6361/202346832</a>. 142562023-09-03T22:01:15Z2026-07-08T06:45:55Z